Algorithms.

The article presents mathematical procedures using Legendre functions for cases involving arguments larger than one. The integer Legendre 1 procedure is said to generate the associated Legendre functions of the first kind. Integer Legendre 2 generates associated Legendre functions of the second kind to d significant digits. The integer Legendre 3 generates the Legendre functions of the second kind to d significant digits and stores in the array Q. Legendre 1 procedure evaluates the Legendre functions to d significant digits. Other procedures include Legendre 2, conical and toroidal.